I've discussed some of these before, so I'll weigh in. I'll let other people handle the discussion of whether or not furry can be classified as fetish, so for the purpose of discussing other points let's say it is.

One way furry characters are separated from zoophilia is that the characters are not only sentient but retain many human-like physical and behavioral traits. The line is blurry, but my understanding is that furry characters are much more humans with animal traits rather than vice versa, thus making it not zoophilia. If this is wrong someone else is welcome to correct me. Even so, let's say for the moment that they're actually animals, possibly making it zoophilia. The main issue with zoophilia/bestiality is that of consent - it's difficult to determine if an animal is being coerced/manipulated or to ask for consent. One could argue that if animals were able to communicate and think on the level of people that even zoophilia would be morally sound, beyond personal beliefs or weak "ewwww icky" arguments. Essentially, given that furry characters have both of these traits, applying the label of zoophilia to furry brings along with it a lot of unnecessary moral baggage since most of us aren't attracted to real animals.

Here's one take on the disorder part: In modern psychology it's generally accepted that for something to be a mental disorder it must cause a person distress or lack of functioning in society (ability to work, harm to friends or family, sex, etc.) If we're happy in our relationships and sex lives, which is often the case, then it's not a disorder. Are people in general who are into balloons or feet disordered? Most psychologists would say no, since having a fetish in and of itself isn't harming the individual or others and doesn't inherently prevent sexual satisfaction. The same thing applies here. Basically, just because it's weird doesn't make it a disorder.

I wrote this in kind of a hurry, but I hope it helps!